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Study Guides > Prealgebra

Dividing Whole Numbers in Applications

Learning Outcomes

  • Translate word phrases that represent division into mathematical expressions
  • Use division to solve word applications
  • Use both division and multiplication

Translate Word Phrases to Math Notation

Earlier in this section, we translated math notation for division into words. Now we’ll translate word phrases into math notation. Some of the words that indicate division are given in the table below.
Operation Word Phrase Example Expression
Division divided by quotient of divided into [latex]12[/latex] divided by [latex]4[/latex] the quotient of [latex]12[/latex] and [latex]4[/latex] [latex]4[/latex] divided into [latex]12[/latex] [latex]12\div 4[/latex] [latex-display]\frac{12}{4}[/latex-display] [latex-display]12\text{/}4[/latex-display] [latex]4\overline{)12}[/latex]

example

Translate and simplify: the quotient of [latex]51[/latex] and [latex]17[/latex]. Solution:

the quotient of 51 and 17   -   The word quotient tells us to divide

translate   -   [latex]51\div 17[/latex]

divide   -   [latex]3[/latex]

We could just as correctly have translated the quotient of [latex]51[/latex] and  [latex]17[/latex] using the notation [latex]17\overline{)51}[/latex]   or  [latex]\frac{51}{17}[/latex].

   

Divide Whole Numbers in Applications

We will use the same strategy we used in previous sections to solve applications. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify it to get the answer. Finally, we write a sentence to answer the question.

example

Cecelia bought a [latex]\text{160-ounce}[/latex] box of oatmeal at the big box store. She wants to divide the [latex]160[/latex] ounces of oatmeal into [latex]\text{8-ounce}[/latex] servings. She will put each serving into a plastic bag so she can take one bag to work each day. How many servings will she get from the big box? Solution We are asked to find the how many servings she will get from the big box.
Write a phrase. [latex]160[/latex] ounces divided by [latex]8[/latex] ounces
Translate to math notation. [latex]160\div 8[/latex]
Simplify by dividing. [latex]20[/latex]
Write a sentence to answer the question. Cecelia will get [latex]20[/latex] servings from the big box.
  In the following video we show another example of how to translate a situation into an algebraic expression. https://youtu.be/y2K-S3tscz0 Now that we have practiced using both multiplication and division to solve application problems, let's combine both skills to answer the next question.

Example

To save money and reduce waste, Frances bought a giant box of crackers with the plan to divide them up into small bags to take to school with her every day. The box contains [latex]48[/latex] oz. of crackers. Answer the following questions about Frances and her crackers: 1) How many [latex]2[/latex] oz. bags of crackers can Frances make from the big bag? 2) If there are [latex]150[/latex] calories in a [latex]1[/latex] oz serving of crackers, how many calories are each 2 oz. bag?

Answer: 1. We are asked to find how many [latex]2[/latex] oz. bags can be made from [latex]48[/latex] oz.

Write a phrase. [latex]48[/latex] ounces divided by[latex]2[/latex] ounces
Translate to math notation. [latex]48\div 2[/latex]
Simplify by dividing. [latex]24[/latex]
Write a sentence to answer the question. Frances will get[latex]24[/latex] servings from the big box.
2. We are asked how many calories are in each [latex]2[/latex] oz. bag of crackers.
Write a phrase. [latex]150[/latex]  times [latex]2[/latex]
Translate to math notation. [latex]150\cdot 2[/latex]
Simplify by multiplying. [latex]300[/latex] calories
Write a sentence to answer the question. There are [latex]300[/latex] calories in each [latex]2[/latex] oz. bag of crackers.

In the following video we show another example of how to translate a situation that contains both multiplication and division into an algebraic expression. https://youtu.be/DneLJVZDL7k

Licenses & Attributions

CC licensed content, Original

  • Divide and Multiply Whole Numbers to Solve Applications. Authored by: James Sousa (Mathispower4u.com) for Lumen Learning. License: CC BY: Attribution.
  • Divide Whole Numbers to Solve Applications. Authored by: James Sousa (Mathispower4u.com) for Lumen Learning. License: CC BY: Attribution.

CC licensed content, Shared previously

  • Question ID: 144450, 144646. Authored by: Alyson Day. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.

CC licensed content, Specific attribution